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Welcome

This is a template to create an Instructional Design Document of the concept you have selected for creating animation. This will take you through a 5 section process to provide the necessary details to the animator before starting the animation.

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Welcome

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  1. This is a template to create an Instructional Design Document of the concept you have selected for creating animation. This will take you through a 5 section process to provide the necessary details to the animator before starting the animation. The legend on the left will indicate the current status of the document. The Black coloured number will denote the current section, the Turquoise color would denote the completed sections, and the Sky bluecolor would denote the remaining sections. The slides having 'Instructions' would have a Yellow box, as shown on the top of this slide. Welcome 1 2 3 4 5

  2. Repetition CodeThe simplest error correcting code Binary Symmetric Channel Prof. Saravanan Vijayakumaran

  3. Definitions and Keywords 1 Bit – A binary digit which can take the value 1 or 0. Channel – The medium through which information transfer takes place. Noisy Channel –A channel which may modify the information which is transmitted through it. Binary channel – A channel which takes bits as input and produces bits as output. Error – An error is said to have occurred if the received information does not match the transmitted information. Errors are caused by noise in the channel. Bit Error – If the channel changes a bit which is transmitted over it, a bit error is said to have occurred. 2 3 4 5

  4. Definitions and Keywords 1 Single Bit Error – Suppose a string of bits is transmitted through a noisy channel. A single bit error is said to have occurred if the channel changes only one of the bits, i.e. the transmitted bit string and the received bit string differ only in one bit. Double Bit Error - Suppose a string of bits is transmitted through a noisy channel. A double bit error is said to have occurred if the channel changes only two of the bits, i.e. the transmitted bit string and the received bit string differ only in one bit. Binary Symmetric Channel (BSC) – A common channel model used in coding theory and information theory to represent a noisy channel. The inputs and outputs to the BSC are the bits 1 and 0. An input bit arrives without change at the output or is flipped with some probability. Crossover Probability – The probability with which a bit at the input of the BSC is flipped. 2 3 4 5

  5. INSTRUCTIONS SLIDE Concept details: 1 2 • In this section, provide the stepwise detailed explanation of the concept. • Please fill in the steps of the explanation of the concepts in the table format available in the slides to follow (see the sample below). • Resize the table dimensions as per your requirements. 3 4 5

  6. INSTRUCTIONS SLIDE Concept details: 1 2 • In this animation, we want to show the operation of the repetition code for two types of channels • A channel which introduces a fixed number of errors. Although the channel introduces a fixed number of errors, position of the errors is not fixed. For example a channel which changes only one bit in the transmitted bit string. So if 111000 is the information transmitted, the received bit string may be 101000 or 111100 or.... • The binary symmetric channel 3 4 5

  7. INSTRUCTIONS SLIDE Concept details: Step 1 1 2 • The user can select between the fixed error channel and the binary symmetric channel. Once he selects the type of channel, there will be five information bits 10101 • Each bit will be repeated three times as it passes through the block titled Repetition Encoder. Make sure the three repetitions of each bit appear together and there is a delay between the repetitions of different bits 3 4 5

  8. INSTRUCTIONS SLIDE Concept details: Step 2 1 2 • The repeated bits are passed through a block titled Noisy Channel. The type of channel (single error, double error, binary symmetric channel) is chosen by the user. The errors are shown in red. 3 4 5

  9. INSTRUCTIONS SLIDE Concept details: Step 3 1 2 • The bits which have passed through the channel are decoded by a block called the Majority Vote Decoder(MVD). The MVD takes three bits as input and outputs the majority of the three bits as the output. 3 4 5

  10. Interactivityand Boundary limits 1 2 Number of repetitions can be from 2 to 7. Larger values cannot be accommodated in the screen. The user can change the number of times a bit is repeated. For eg, she can choose 5 instead of 3. 3 The number of errors a noisy channel introduces can be changed by the user. This applies only to the channel which introduces a fixed number of errors. For eg, the number of errors introduced by the channel can be 2 instead of 1 as shown in the figure above. Number of errors can be from 1 to 10. 4 The crossover probability can be from 0 to 0.5. If the channel type chosen by the user is the binary symmetric channel, the user can change the crossover probability. 5

  11. Links for further reading 1 [1] “Elements of Information Theory”, by Thomas Cover and Joy Thomas [2] Repetition Code on Wikipedia http://en.wikipedia.org/wiki/Repetition_code [3] Majority Logic Decoding on Wikipedia http://en.wikipedia.org/wiki/Majority_logic_decoding 2 3 4 5

  12. Thank you

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